Add comments on of Potemine's j-invariants

We believe there was an ambiguity between our naming of j-invariants,
basic j-invariants and jk-invariants, as we follow Potemine's
convention, which differs from Papikian's. Consequently, we remove the
ambiguity in a note in the docstring.

Author: kryzar

src/doc/en/reference/references/index.rst

@@ -5110,6 +5110,10 @@ REFERENCES:
              B46f,
              https://eudml.org/doc/121696
 
+.. [Pap2023] Mihran Papikian, *Drinfeld modules*.
+             Graduate Texts in Mathematics, 206,
+             Springer International Publishing, Cham, 2023.
+
 .. [PALP] Maximilian Kreuzer, Harald Skarke: "PALP: A Package for
           Analyzing Lattice Polytopes with Applications to Toric
           Geometry" omput.Phys.Commun. 157 (2004) 87-106

src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py

@@ -1510,6 +1510,26 @@ def j_invariant(self, parameter=None, check=True):
         :meth:`basic_j_invariant_parameters` for computing the list of
         all basic `j`-invariant parameters.
 
+        .. NOTE::
+
+            In [Pap2023]_, Papikian follows a slightly different
+            convention:
+
+            - His `j`-invariants (see Definition 3.8.7) correspond to
+              our basic `j`-invariants, as defined above.
+            - His *basic* `j`-invariant (see Example 3.8.10) correspond
+              to our `j_k`-invariants, as implemented in
+              :meth:`jk_invariants`.
+
+            We chose to follow Potemine's convention, as he introduced
+            those objects in [Pot1998]_. Theorem 2.2 of [Pot1998]_ or
+            Theorem 3.8.11 of [Pap2023]_ assert that two Drinfeld
+            `\mathbb F_q[T]`-modules over `K` are isomorphic over the
+            separable closure of `K` if and only if their basic
+            `j`-invariants (as implemented here) coincide for any
+            well-defined couple of tuples `((k_1, k_2, \ldots, k_n),
+            (d_1, d_2, \ldots, d_n, d_r))`, .
+
         INPUT:
 
         - ``parameter`` (tuple or list, integer or NoneType; default:
@@ -1536,11 +1556,6 @@ def j_invariant(self, parameter=None, check=True):
 
         OUTPUT: the `j`-invariant of ``self`` for the given parameter.
 
-        REFERENCE:
-
-        The notion of basic `j`-invariant was introduced by Potemine in
-        [Pot1998]_.
-
         EXAMPLES::
 
             sage: Fq = GF(25)